# Elementary Number Theory – Helps solve this proof using the well command principle

Let $$a_1, a_2, …, a_n ∈ Bbb {N}$$ . Prove that there is $$l ∈ Bbb {N}$$ such as $$a_i | l$$ for everyone $$i ∈ {1,2, …, n }$$ and if $$x B Bbb {N}$$ is such that each $$a_i$$ Split $$x$$then $$l | x$$.

Hi, I know this proof includes a good command method method, maybe to find $$l$$. But I am very confused as to how to solve it. Especially with the second half of the question. All answers are appreciated.